Criteris For Handling

Journal of Terramechanics

Journal of Terramechanics 43 (2006) 43–67

www.elsevier.com/locate/jterra

Criteria for handling measurement P.E. Uys *, P.S. Els, M.J. Thoresson Department of Mechanical and Aeronautical Engineering, University of Pretoria, Pretoria 0002, South Africa Accepted 24 August 2004 Available online 25 September 2004

Abstract Both handling and ride comfort play an important role in the performance of a vehicle, usually resulting in a compromised suspension. To improve this situation, a two-stage, semi-active hydro-pneumatic spring–damper system has been developed. The suspension system enables either good ride comfort for a compliant suspension or good handling when changed to a hard setting. The question that arises is, what measures can be applied to determine when a switchover between the two settings should occur. The frequency weighted mean square value of the vertical acceleration is a well-known criterion for ride comfort. For handling, several criteria have been put forward, which are to a more or lesser extent dependent on driver input. This paper considers the metrics that have been used for measuring handling and pays special attention to roll angle as a valid criterion. Results of tests performed on three different vehicles are presented. The results indicate that roll angle, lateral acceleration and yaw rate are interrelated for the tracks investigated and this is apparently also true for severe handling manoeuvres such as the double lane change. These observations suggest that roll angle is a suitable metric to measure handling and that it can be used to determine the moment of switchover if limits of acceptability are set. Ó 2004 ISTVS. Published by Elsevier Ltd. All rights reserved. Keywords: Handling criteria; Roll angle; Semi-active suspension; Off-road

*

Corresponding author. Tel.: +27 12 420 2254; fax: +27 12 362 5087. E-mail address: [email protected] (P.E. Uys).

0022-4898/$20.00 Ó 2004 ISTVS. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.jterra.2004.08.005

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1. Introduction A semi-active hydro-pneumatic damper and spring system has been developed for a leisure vehicle that is used both on highways and rough off-road terrain. The suspension can be switched between a soft damper soft spring state, and a hard spring hard damper state, to ensure comfortable secure handling under all road circumstances. The moment of switchover has to be determined from the value of objective precise criteria of both comfort and handling. The root mean square value of the vertical acceleration is known to be a good criterion of comfort, and levels of acceptance in terms of comfort and safety have been determined [1]. A single, unambiguous objective criterion for handling, has however eluded the vehicle science community despite numerous studies pertaining to the topic. As Vlk [2] notes with respect to truck-trailer devices, ‘‘It is most desirable to define evaluation criteria for the handling performance of vehicle combinations, both for steady state and transient driving behaviour’’. The aim of this paper is to summarise suggestions and conclusions of research on handling criteria, and to present and discuss the results of tests performed to determine a handling norm, which will be suitable for handling optimisation and can be calibrated to determine the moment of switchover for a semi-active suspension.

2. Literature survey 2.1. Yaw rate and lateral acceleration Horiuchi et al. [3] determined that drivers focus attention on yaw angle rather than on lateral position error, Ye, for steering a two wheel steering system car. For a four wheel steering system car Ye becomes more important. Handling (steer response) is measured in terms of yaw rate and lateral acceleration for handling characteristics of four wheel active steering vehicles over a wide manoeuvring range of lateral and longitudinal accelerations [4]. Sharp and Pan [5] comment that a vehicle with no body roll in general has better steering behaviour than one that rolls. Handling performance could thus be improved if the vehicle is made stiffer in roll by stiffening of anti-roll bars. 2.2. Roll angle Metrics used in subjective/objective driver-handling correlations for J-turns (step steer input) by Crolla et al. [6] include: peak lateral acceleration response time, peak road wheel steer angle and response time, peak yaw and roll rate and response time and peak value of torque applied to steering wheel and response time. The authors point to the importance of frequency response results (lateral acceleration gain, yaw gain, steering gain, steering phase) and suggest that they could be of greater value in assessing vehicle response than has to date been foreseen. These metrics, along with the change in side slip with respect to the change in lateral acceleration, were rated by

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drivers participating in the tests, as uniform and unequivocal indicators of steering response required. From an investigation on the correlation between the different metrics, Crolla et al. found that, over smooth roads, the degree of roll angle in cornering correlates with lateral acceleration phase and yaw rate in a J-turn and with lateral acceleration gain, yaw gain and roll rate in steady state turning. Controllability during a single lane change correlated with yaw rate response time and steering gain [6]. These observations of Crolla et al. suggest that the degree of roll angle is related to lateral acceleration and yaw rate, which are both effective inputs for driver response. 2.3. Lateral transient response to step input Lateral transient response to step input is a frequently adopted measure for assessing handling characteristics according to Reichardt [7]. 2.4. National Highway Safety Administration: roll over metrics and rating [8] Since roll over is to an extent related to handling, although handling capability and roll over aptitude are not similar, roll over considerations as deducted from the National Highway Safety Administration (NHTSA) survey was investigated. Under handling the response properties of a vehicle perceived and experienced by the driver acting as the controller would be considered. Roll over on the other hand pertains to the tendency of the roll amplitude and motion of the vehicle to increase progressively due to a manoeuvre induced disturbance. In an effort to regulate roll over propensity, NHTSA required a safety standard ‘‘that would specify minimum performance requirements for the resistance of vehicles to roll over in simulations of extreme driving conditions’’. The conclusion was that ‘‘vehicle roll over response is dominated by the vehicles rigid body geometry with dynamic contributions from suspension effects’’. NHTSAÕs analysis [8] of 100 000 single-vehicle roll over crashes eventually focused on two static measurements: tilt table angle (the angle at which a vehicle will begin to tip off a gradually tilted platform) and critical sliding velocity (the minimum velocity needed to trip a vehicle which is sliding sideways) – both measurements address situations in which a vehicle encounters something that trips it into roll over (a curb, soft dirt, the tire rim digging into the pavement). Taking into account safety objectives, the following vehicle stability metrics were considered as having a potentially significant role in roll over: centre of gravity height, static stability factor (SSF), tilt table ratio, side pull ratio, wheelbase, critical sliding velocity, roll over prevention metric, braking stability metric and percentage of total weight on the rear axle. A vehicle stability metric in this case indicates a measured vehicle parameter thought to be related to the vehicleÕs likelihood of roll over involvement. The following aspects were considered for roll over rating.

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2.4.1. Static stability factor Present roll over rating: static measurement of half a vehicleÕs track width divided by its height at its centre of gravity [9]. 2.4.2. J-turn and fish hook manoeuvres In order to warn the public about a vehicleÕs stability with specific reference to roll over, NHTSA has chosen the J-turn and the fishhook manoeuvre to rate a vehicleÕs performance. ‘‘They are the limit manoeuvre tests that NHTSA found to have the highest levels of objectivity, repeatability and discriminatory capability’’. The intention is that ‘‘vehicles will be tested in two load conditions, using the J-turn at up to 97 km/h and the fish hook manoeuvre at up to 80 km/h’’. ‘‘Light load conditions will be provided by the test driver who will be the test vehicleÕs sole occupant. Heavy load conditions will be created by adding a 79.5 kg mannequin to each rear seating position’’. ‘‘The dynamic manoeuvre test performance will be used to rate resistance to untripped rollovers on a qualitative scale such as A – for tip-ups, B – for tip-up in one manoeuvre, C – for tip-ups in two manoeuvres, etc.’’ [8]. ‘‘The reverse steer of the fishhook manoeuvre will be timed to coincide with the maximum roll angle to create an objective Ôworst caseÕ for all vehicles regardless of differences in resonant roll frequency’’. In response to its request for development of a dynamic test for roll over resistance the following limiting values for good roll over resistance were mentioned by general motors (GM): (a) quasi-static centrifuge test tip-up threshold of at least 0.9g; (b) maximum lateral acceleration in a circular driving manoeuvre of at least 0.6g; and (c) a stability margin (a) and (b) at least 0.2g or 1.5/wheelbase (m2). GM estimated that a centrifuge measurement of 0.9g would correspond to a SSF of 1.06. NHTSA however, estimated the centrifuge measurement as corresponding closer to a SSF of 1.00, based on comparisons with tilt table tests with an allowance for the vertical load error inherent with the tilt table. Ford suggested lane change manoeuvres producing a maximum lateral acceleration of 0.7g [8]. 2.5. NHTSA and vehicle handling In the same survey NHTSA posed the question: Should measures of vehicle handling be reported so that consumers can be aware of possible trade-offs? What indicators of vehicle handling would be appropriate to measure, and how should this consumer information be reported? The following responses are documented: 2.5.1. Steady state lateral acceleration and lateral transient response Nissan recommended that NHTSA measure handling rather than roll over resistance, on the basis that the fishhook test may be too severe for the purposes of consumer information, and that Nissan had no data regarding the correlation of fishhook test performance to real-world crashes. It suggested a steady state lateral acceleration test and a lateral transient response test.

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2.5.2. ISO 3388 part 2
Optimised cornering capability and ‘‘limit condition performance’’. Daimler-Chrysler (DC) addressed the question directly by stating that the recommended ISO 3388 PART 2 test does not give incentives for negative trade-offs, but rather encourages optimised cornering capability and ‘‘limit condition performance’’ by giving lower ratings for ‘‘bad handling’’. In its recommendation on the ISO 3388 PART 2 test, Continental-Tyres actually described it as a handling test.
Entry speed and peak-to-peak yaw rate. Toyota suggested using the ISO 3388 PART 2 test as a handling test with both entry speed and peak-to-peak yaw rate as performance criteria. The peak-to-peak yaw rate would reflect on the yaw stability of the vehicle.
Centrifuge and steady state lateral acceleration tests. GM also recommended the centrifuge test, but suggested combining its results with a driving test of steady state maximum lateral acceleration to create a stability margin and set a lower limit for handling. In addition to static and dynamic roll over resistance tests, the Consumer Union (CU) recommended a steady state lateral acceleration test on a skid pad and ‘‘track-type tests to assess the vehicleÕs controllability, response and grip’’.
Evaluation of double lane change. Daimler-Chrysler, Mitsubishi, VW, BMW and Continental-Tyres recommended the ISO 3388 PART 2 closed-loop tight double lane change test as the best dynamic roll over test, but also described it as a handling test. Toyota, UMTRI, Nissan, VW and Ford recommend a separate handling test distinct from the roll over rating with particular emphasis on yaw stability and Electronic Stability Control.
Double lane change vs. fishhook and J-turn. Although all roll over resistance manoeuvres are influenced by both a vehicleÕs handling characteristics and its resistance to tip-up, it appears that handling dominates the Double Lane Change manoeuvres but is less important for the J-Turn and Fishhook manoeuvres. The Double Lane Change manoeuvres are better for studying emergency vehicle handling than roll over resistance. Clean runs of the CU and ISO 3388 tests are not limit manoeuvres in the sense of the J-Turn and Fishhook because they cannot measure tip-up after the vehicleÕs direction control is lost. One way to characterize manoeuvres is by the number of major steering movements they involve. The J-Turn has just one major steering movement, the initial steer. A Fishhook has two major steering movements, the initial steer and the counter steer. A double lane change has four major steering movements, the initial lane change steer, the second lane change steer, the recovery steer, and the stabilization steer, plus some minor steering movements. These additional major steering movements increase the influence of handling for Double Lane Change results compared to J-Turn and Fishhook manoeuvres.
Highest clean run. NHTSA comments: ‘‘double lane change manoeuvres scored on the basis of highest ‘‘clean’’ run speed had no value as dynamic tests of roll over resistance’’. For a

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sample of test vehicles, there was actually an inverse relationship between double lane change speed scores and the incidence of tip-up in more severe manoeuvres that induced tip-up. The test vehicle that tipped-up the most often in other manoeuvres and at a consistently lower tip-up speed than other test vehicles, would be rated the best vehicle for roll over resistance by the CU Short Course or ISO 3388 Part 2 double lane change on the basis of maximum clean run speed. These tests measure a type of handling performance but do not measure roll over resistance’’ [8]. 2.6. Effective dynamic wheel loads Holdmann and Holle [10] use effective dynamic wheel loads as a measure of driving safety. By taking into account the RMS values of the dynamic loads, a hard damper system assures driving comfort as well as driving safety up to 4 Hz, a soft damper system assures good results for both at frequencies from 4 to 8 Hz and at higher frequencies a soft damper minimizes body movement and a hard damper minimises dynamic wheel loads. They state that different damping systems have a very small effect on lateral dynamics. 2.7. Pitch motion and roll angle as measures of steering stability Choi et al. [11] indicate pitch motion and roll angle as measures of steering stability in the evaluation a semi-active Electro Rheological suspension system. 2.8. RMS tyre contact force as an indication of wheel hop and road holding capability For experimental comparison of passive, semi-active on/off and semi-active continuous suspensions, Ivers and Miller [12] use RMS tyre contact force as an indication of wheel hop and road holding capability. 2.9. Standardisation of parameters with respect to steering wheel activity and regression of linear combinations Data and Frigero [13] note that it is possible to obtain valid objective indications of vehicle handling quality by comparing subjective evaluations by drivers of steady state circular tests, step steering wheel input and double lane change with objective parameters. The following objective parameters were proposed as representative of vehicle behaviour: lateral acceleration versus steering wheel angle, yaw velocity versus steering wheel angle, lateral acceleration versus yaw velocity, roll angle versus lateral acceleration and sideslip angle versus steering wheel angle. Parameters, which are considered functions of lateral acceleration, are standardised with respect to steering wheel activity, which is strongly influenced by driver

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activity. The objective parameters representative of vehicle behaviour are the values of the regression lines and their angular coefficients at 0.4g lateral acceleration. It was found that there is no correlation between a single partial rating and a single objective indicator. Linear combinations of the objective indicators were used to find a maximum regression coefficient R2. This resulted in a series of equations called partial indices that predict a subjective rating, given objective parameters as input. From this paper the most important parameters related to handling performance are roll angle, lateral acceleration and roll velocity, which are related to steering wheel angle, yaw velocity and lateral acceleration. 2.10. Steering wheel angle, dynamic weight transfer and roll rate In its presentation of roll over propensity testing of light vehicles [14], NHTSA suggests measuring steering wheel angle during a simple step steer test, a J-turn and a fishhook turn; measuring dynamic weight transfer during a double lane change and measuring the roll rate for a steering rate of 1000°/s in a J-turn and for 720°/s during a fish hook turn. 2.11. Detection of instability, roll and roll moment and lateral acceleration measurement In his studies on onset of roll over, Dahlberg [15] states that for the detection of instability the most frequently used method is in-vehicle measurement of lateral acceleration, followed by comparison to the steady state roll over threshold (SSRT) (where the accelerometer is mounted on the front axle). SSRT is considered [15] the maximum value of the lateral acceleration that the vehicle may resist during steady state driving in order not to roll over. It is a sufficient but not necessary requirement for roll over to occur. The static stability factor (SSF) = 1/2 (average front and rear track width) divided by total centre of gravity (CG) height, is a first order approximation to SSRT, it is the least conservative estimation of roll over propensity and thus predicts a higher threshold. SSRT becomes smaller as more flexibility is introduced in the analysis (suspension compliance, lateral shift of CG, flexibility of tyres, chassis and frame flexibility). Dahlberg refers to another analysis approach, used by an author whom he refers, taking roll and roll moment into account in addition to lateral acceleration. This approach gives a better understanding of individual axle roll resistance and enables him to determine that the vehicle can roll over when the lateral acceleration is larger than the value corresponding to wheel lift. Roll over does not take place during steady state driving, but during transient manoeuvres. SSRT is a best-case measure of roll stability, whereas a worst-case measure is needed. Therefore Dahlberg defines the Dynamic Roll over threshold as ‘‘the minimum absolute peak value of lateral acceleration of all manoeuvres bringing the vehicle to roll over’’. This defines a worst-case measure of roll stability. It is a necessary but not sufficient condition for roll over [15].

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2.12. Experiments to determine untripped roll over propensity Garrot et al. [16] describes experiments to determine untripped roll over propensity: 1. Different categories of vehicles are used – passenger cars, light delivery trucks, vans, sport utility vehicles. 2. Vehicle characterisation is done by means of manoeuvres designed to determine fundamental handling properties. 3. For vehicles with relative higher roll over propensity, measures are designed to produce two-wheel lift off. 4. Vehicle characterisation manoeuvres include: pulse steer, sinusoidal sweep, slowly increasing steer, slowly increasing speed (at constant steering angle up to 0.7g lateral acceleration). 5. Rollover propensity is determined from the following manoeuvres: J-turn, J-turn with pulse braking, a Fishhook manoeuvre using a fixed 270° initial steering input, a Fish hook manoeuvre using an initial steering angle 7.5 times the overall steering ratio of a given vehicle and resonant steer. 6. They relate the degree of lift off (minor, moderate, major) and vehicle manoeuvring steer score, to roll over stability metrics (SSF, tilt table ratio and critical sliding velocity). 2.13. Steering factor Uffelman [17] relates handling to the steering factor p¼

C a f lf ; C a r lr

ð1Þ

where Ca f is the cornering stiffness of the front tyres; Ca r the cornering stiffness of the rear tyres; lf the distance from the front axle to the centre of gravity and lr the distance from the rear axle to the centre of gravity. The limit of instability in handling is considered at the point of a level tangent of the steering wheel angle versus the lateral acceleration graph. Uffelman considers performance characteristics for quasi-steady-state cornering and braking. He shows that for a passenger car the ratio p and steering wheel angle increase sharply for a lateral acceleration around 0.5g for braking at 0.1g and between 0.4g and 0.5g for braking between 0.2g and 0.4g where the limit of adhesion is approached. These limits are dependent on braking balance and load conditions. 2.14. Sensitivity of yaw rate response El-Gindy and Mikulcik [18] indicate that yaw rate gain (ratio of yaw rate to steering angle) increases with increasing speed, that the sensitivity of yaw rate gain to steering input frequency increases with increasing speed, but the sensitivity to speed increase, decreases as speed increases. The effect of mass, moment of inertia, front

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and rear cornering stiffness and location of centre of gravity is also addressed. They conclude that the strongest parameter on the yaw rate gain is location of the centre of gravity. The cornering stiffness of the front wheels also has a more pronounced effect than the rear cornering stiffness. 2.15. Yaw rate and side slip frequency response Starkey [19] derives yaw rate and sideslip frequency response for a highway vehicle from a yaw-plane handling model valid in the linear range. 2.16. Lateral force Suspension technology capable of reconciling handling, stability and ride comfort has been designed by Toyota Motor Company. The rear and front suspension settings react to lateral force input to the tyres [20]. 2.17. Quadratic forms of state variables In order to objectively evaluate handling performance, Harada [21] derives stability criteria for typical lane change cases and running against cross winds, applying a linear preview control model to the driver and a bicycle model of the vehicle. The performance index is composed of the weighted mean square values of state variables such as the course deviation, steering correction angle, yaw velocity and lateral velocity. Stability criteria consist of the steering control gain and steering time constant, which are obtained numerically for a closed loop system by the Hurwitz stability criteria. 2.18. Handling performance of a truck-trailer vehicle In his survey of the handling performance of truck-trailer vehicles, Vlk [2] mentions the following criteria that were used: lateral stability and movement, Hurwitz criterion for stability, yaw angle, lateral displacements in tyre road contact paths, lateral play at the hitch, side amplitude of trailer, frequency of trailer yaw oscillations, yaw rate gain, lateral axle deviation, side slip angle, overturning risk, lateral acceleration, change of wheel vertical loads, longitudinal tyre slip and cornering forces as a result of directional response due to braking. He also mentions experiments by Zhukov who ascertained that the roll rotation of a trailer was accompanied by a lateral displacement of both truck and trailer from their direct path. The most outstanding correlation found was between trailer roll and yaw. 2.19. Stability during severe manoeuvres EL-Gindy and Ilosvai [22] mentions a study of Yim et al. that indicated that the slip-ratio of the front wheels relative to that of the rear wheels correlated with stability. El Gindy investigated lane change and braking manoeuvres on dry and wet

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asphalt and uses lateral acceleration, yaw rate, lateral displacement and heading angle to determine stability. It is apparent from this survey that measurement of vehicle handling is not a clearcut matter. The aim of the survey was to determine whether a metric has been described that could be used to decide when a switch over from a soft to a hard suspension setting and vice versa should occur. It should also be such that it can be used to optimise the suspension settings. It is concluded from the information presented here that no such unambiguous metric is apparent. There are, however, some parameters that are worth considering and these were used to direct the experimental investigation. 3. Experimental investigation 3.1. The experimental setup In previous simulation studies [23] it was shown that measurements of roll angle can be used for optimisation of suspension settings. Choi et al. [11], Data and Frigero [13] and Crolla [6] also refer to roll angle as a measure of handling, as does the NHTSA survey and Vlk [2]. Other parameters which have prominence in handling quality measurements are lateral acceleration, dynamic weight transfer, roll rate, maximum entry speed to a clean run on a double lane change and peak to peak yaw rate. Since dynamic weight transfer is very dependent on the tyre model used in simulations and direct measurement poses complications, this property is disregarded for the moment. For suspension control it is also argued that in general the drivers do not drive vehicles at their performance limits, since they are not trained test drivers. Preferably parameters should be sought that can be measured during regular off-road driving, on highways and over mountain passes requiring greater handling skills. Also experience with the optimisation of suspension settings for both handling and comfort, has indicated that convergence to an optimum can readily be obtained if optimisation is first performed with respect to handling and then with respect to ride comfort, with boundaries set on the handling parameters [23]. These limits of secure handling as experienced by drivers, have not been quantified as is the case with comfort [1]. With this background in mind an experiment was designed in which three vehicles were test driven by four drivers. The vehicles consisted of a Ford Courier LDV, a VW Golf 1 Chico and a VW Golf 4 GTi. The drivers included a student (23), a woman (50), a man in his thirties (35) and one in his forties (46). The vehicles were equipped with accelerometers, displacement sensors, roll angle sensors and equipment to measure speed. The measurements taken are indicated in Table 1. Measurements were made on two tracks at Gerotek Test Facility outside Pretoria in South Africa: a ride and handling track and a dynamic handling track for light vehicles. The track particulars are listed in Table 2. A single run on a rough track representing off-road conditions was also performed. These tests are considered preliminary to establish a procedure and base of comparison for future tests that might also include a constant radius and double lane change test and will be supported by a larger number of drivers.

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Table 1 Summary of measurements Instrument

Position

Measurement

Accelerometer

Front centre

Lateral acceleration Longitudinal acceleration Vertical acceleration

Accelerometer

Right back

Lateral acceleration Longitudinal acceleration Vertical acceleration

Accelerometer

Left back

Lateral acceleration Longitudinal acceleration Vertical acceleration

Angle sensor

Roll angle Yaw angle

Gyro

Roll rate Yaw rate Pitch rate

Displacement Speed sensor

Steering wheel angle Longitudinal speed

3.2. Results and discussion The results are given in Appendices A–C. Figs. A.1–A.5 refer to dynamic handling performance of a Golf GTi as related to the different drivers. Appendix B concerns the performance of the different vehicles considering all the drivers in order to obtain a global impression of vehicle performance on both the dynamic handling and ride and handling tracks. Only the results of the Courier and GTi are shown since these indicated the lowest and highest performance levels. Appendix C shows some results of tests performed on a Land Rover during a double lane change and also corresponding results obtained by simulations using the dynamic package ADAMS. The latter is included to determine if the same trends as those observed in the other vehicle tests also apply. The figures documented relate roll angle, lateral acceleration and yaw rate and also include some information on the effect of speed and a G–G plot.
Considering Figs. A.1 and A.2 it is clear that the trends in the relations forward acceleration vs. lateral acceleration, yaw rate vs. roll rate, yaw rate vs. lateral acceleration and roll angle vs. lateral acceleration, are the same. This has been verified for the other drivers. The limiting values do however differ, for example some 30% for the upper limit of the lateral acceleration.
The same trends are also observed for different vehicles although the absolute values differ (compare Figs. B.1, B.2, B.5 and B.6).
Referring to the yaw rate vs. roll angle, yaw rate vs. lateral acceleration and roll angle vs. lateral acceleration graphs in Figs. A.1 and A.2, linear dependency is observed.

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Table 2 Test track specifications Ride and handling track Designed to evaluate ride and handling characteristics and driveline endurance of wheeled vehicles Distance: 4.2 km Turns: 13 left, 15 right Max gradients: 5% Track surface: mooth concrete with irregular spaced grooves or water dissipation and raction

Dynamic handling track (light vehicles) Designed to evaluate the high speed handling characteristics of light vehicles Distance: 1.68 km (excluding spiral curve) Track surface: Asphalt Coefficient of friction: l = 0.7 Scrim (average) or 0.4 brake force coefficient wet (average) Entails a wave curve, trapezium curve, spiral curve, kink/hairpin combination


The linear dependence amongst the indicated parameters holds true for (i) different drivers (Fig. A.1 compared to Fig. A.2), (ii) different vehicles (Fig. B.1 compared to Fig. B.5 and B.2 compared to Fig. B.6, refer also to Fig. C.1 for yaw rate vs. lateral acceleration and roll angle vs. lateral acceleration) and (iii) different tracks (Compare Fig. B.1, B.2 and Fig. B.5, B.6).

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Table 3 Limiting parameter values Parameter

Ride and handling track

Dynamic vehicle handling track

Roll angle Lateral acceleration front centre Roll rate Yaw rate Steering angle Vehicle speed Longitudinal acceleration

3.5° to +3.5° 1.4g to 1.0g 32°/s to +32°/s 35°/s to +35°/s 60° to +130° 0–120 km/h 0.8g to +0.4g

2° to 2° 1 to 0.7g 6°/s to +8°/s 32°/s to +35°/s 48° to +48° 0–100 km/h 0.4g to +0.5g

Differences in gradients amongst vehicles can be attributed to differences in suspension roll stiffness.
The limiting hyperbolic tendency between lateral acceleration and vehicle speed is apparent from Figs. B.2 and B.6, confirming the applicability of the handling control based on these limits (Toyota).
The off-linear tendency between yaw rate and lateral acceleration for the Ford Courier on the dynamic handling track (Fig. B.1), is due to slippage of the rear wheels, since the vehicle exhibits considerable understeer behaviour that goes into limit oversteer.
The roll angle observed for the Land Rover (Fig. C.1) is considerably larger than that observed for the other vehicles. This can be ascribed to the fact that the centre of gravity of the Land Rover is considerable higher and its suspension is significantly softer than that of the Courier that was driven unladen.
The lateral acceleration and roll angle histograms (Figs. A.3–A.5, B.3, B.4, B.7 and B.8) indicate more clearly the limits in lateral acceleration and roll angle achieved on the various tracks by the different vehicles. It is clear from Figs. A.4 and A.5 that driver B spent more time at the vehicle limits, while driver A (Figs. A.3 and A.4) kept within safe boundaries. The difference in limiting values for the different tracks (see Figs. B.3 and B.4), i.e. 0.77 vs. 1.2 m/s2, some 30%, for B.3 can also be observed. The limits are thus related to the track and vehicle properties.
More noise is observed on the ride and handling track than on the dynamic track. The irregular surface and bumps induce more high frequency motion.
No relation similar to that observed for yaw rate, lateral acceleration and roll angle is observed for roll rate.
The limiting values relating to the tracks on which the tests were performed are listed in Table 3. Lateral acceleration is often considered by analysts as a measure of handling performance. The observed relationship between lateral acceleration and roll angle can be verified by considering the moment distribution of a total vehicle about the roll axis during steady state cornering [24]:

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/¼

Wh1 =g ay ; K / f þ K / r  Wh1

ð2Þ

i.e. linear dependence determined by the roll stiffness. Here ay is the lateral acceleration, K/f is the front roll stiffness of the suspension, K/r the rear roll stiffness, W the weight and h1 the distance from centre of gravity to the roll axis.

4. Conclusion A one to one relationship between lateral acceleration and roll angle has been observed in the case of all drivers of different vehicles on a ride and handling and a dynamic handling track. The range of values of roll angle observed for the tracks referred, is between 3.5° and 3.5°. The investigation concerns an off-road leisure vehicle travelling both off-road and on highways for which a semi-active suspension system is being developed. The aim of the investigation was to find a measure of handling, which can be used to: (i) optimise the suspension settings given a prescribed road and (ii) determine the moment a switchover from a hard to a soft suspension setting and vice versa, should occur. The tests conducted strongly suggest that roll angle is a suitable metric to measure handling. From previous results it is known that roll angle is also suitable for the optimisation of suspension settings given a prescribed road and manoeuvre. If levels of handling acceptance can be determined, this metric can be used as a criterion to ascertain the moment of switchover for a semi-active suspension. Whether the value of the roll angle is a sufficient indicator to determine suspension settings on rough roads, remains to be verified. Future research will include tests on a larger number of vehicles and include more drivers to determine the limits of acceptable roll angle.

Acknowledgements Optimisation related investigations were performed under the auspices of the Multi-disciplinary Design Optimisation Group (MDOG) of the Department of Mechanical and Aeronautical Engineering of the University of Pretoria. The vehicle dynamics simulation for the design of the controllable suspension system is based upon work supported by the European Research Office of the US Army under Contract No. N68171-01-M-5852.

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Appendix A. Results on dynamic performance of a VW Golf4 GTi on a ride and handling track related to different drivers (see Figs. A.1–A.5)

Fig. A.1. Performance related to driver A.

Fig. A.2. Performance related to driver B.

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Fig. A.3. Roll angle histograms for drivers A and B.

Fig. A.4. Lateral acceleration histogram for driver A.

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Fig. A.5. Lateral acceleration histograms for driver B.

Appendix B. Results on dynamic handling performance related to different vehicles for all drivers (see Figs. B.1–B.8)

Fig. B.1. Lateral acceleration, yaw rate and roll angle performance of a Ford Courier on a dynamic handling track.

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Fig. B.2. Lateral acceleration, yaw rate and roll angle performance of a Ford Courier on a ride and handling track.

Fig. B.3. Lateral acceleration (g) and roll angle (°) histograms for a Ford Courier on a dynamic handling track.

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Fig. B.4. Lateral acceleration (g) and roll angle (°) histograms of a Ford Courier on a ride and handling track.

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Fig. B.4 (continued)

Fig. B.5. Lateral acceleration, yaw rate and roll angle performance of a VW Golf4 GTi on a dynamic handling track.

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Fig. B.6. Lateral acceleration, yaw rate and roll angle performance of a VW Golf4 GTi on a ride and handling track.

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Fig. B.7. Lateral acceleration (g) and roll angle (°) histograms for a VW Golf 4 GTi on a dynamic handling track.

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Fig. B.8. Lateral acceleration (g) and roll angle (°) histograms for a VW Golf 4 GTi on a ride and handling track.

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Appendix C. Comparison of simulated and measured results for a Land Rover performing a double lane change (see C.1)

Fig. C.1. Lateral acceleration (m/s2), roll angle (°) and yaw rate (°/s) performance of a Land rover obtained from measurements (regular lines) and simulations (bold dots) in the dynamic package ADAMS.

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